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**Managing Inventory throughout the Supply Chain**

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**Chapter Objectives Be able to:**

Describe the various roles of inventory, including the different types of inventory and inventory drivers. Distinguish between independent demand and dependent demand inventory. Calculate the restocking level for a periodic review system. Calculate the economic order quantity (EOQ) and reorder point (ROP) for a continuous review system. Determine the best order quantity when volume discounts are available. Calculate the target service level and target stocking point for a single-period inventory system. Describe how inventory decisions affect other areas of the supply chain. In particular, be able to describe the bullwhip effect, inventory positioning issues, and the impact of transportation, packaging, and material handling considerations.

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**Inventory Management Functions, forms, and drivers of inventory**

Inventory cost issues Tools: Economic order quantity (EOQ) Reorder point (ROP) and safety stock Dealing with quantity discounts

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**Types of Inventory Cycle stock Safety stock (buffer inventory)**

Anticipation inventory Others Hedge inventories Transportation inventory (pipeline) Smoothing inventories

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**Four Inventory Drivers**

Demand and Supply Uncertainties Safety stock, hedge inventory Demand and Process Volume Mismatches Cycle stock Demand and Capacity Mismatches Smoothing inventory Demand and Supply Lead-Time Mismatches Anticipation inventory, transportation inventory

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**Independent Demand Demand from outside the organization**

Unpredictable usually forecasted Demand for tables . . .

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**Dependent Demand Tied to the production of another item**

Relevant mostly to manufacturers Once we decide how many tables we want to make, how many legs do we need?

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**Two “Classic” Systems for Independent Demand Items**

Periodic review systems Continuous (perpetual) review systems Factors Order quantity (Q) Restocking level (R) Inventory level when reviewed (I)

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**Restocking Levels Periodic Review Continuous Review Periodic Review**

Here RP+L represents the reorder period plus the order lead time, mu is the average demand during that time and sigma is the standard deviation of the demand during that time. Z or zeta is the number of standard deviations chosen to achieve a desired service level. Continuous Review: Here d is the demand rate and L is the lead time for an order to come in. Obviously, variations in the demand and lead time are not accounted for since continuous review allows adjustment for some variation in these values.

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**Periodic Review System (Orders at regular intervals)**

Inventory level 2 4 6 Time

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**Continuous Review System (Orders when inventory drops to R)**

How is the reorder point ROP established? Q Inventory level R Time L-T lead time to get a new order in

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**Comparison of Periodic and Continuous Review Systems**

Periodic Review Fixed order intervals Variable order sizes Convenient to administer Orders may be combined Inventory position only required at review Continuous Review Varying order intervals Fixed order sizes (Q) Allows individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks

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**Order Quantity Q and Average Inventory Level**

As the order quantity doubles so does the average inventory (= Q/2) Q2 Q2 2 Q1 Q1 2

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**What is the “Best” Order Size Q?**

Determined by: Inventory related costs Order preparation costs and setup costs Inventory carrying costs Shortage and customer service costs Other considerations Out of pocket or opportunity cost? Fixed, variable, or some mix of the two?

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**Economic Order Quantity (EOQ) Model**

Cost Minimizing “Q” Assumptions: Uniform and known demand rate Fixed item cost Fixed ordering cost Constant lead time

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**What are the Total Relevant Annual Inventory Costs?**

Consider: D = Total demand for the year S = Cost to place a single order H = Cost to hold one unit in inventory for a year Q = Order quantity Then: Total Cost = Annual Holding Cost + Annual Ordering Cost = [(Q/2) × H] + [(D/Q) × S] Comment: Can explain to students that item cost is considered when evaluating volume discounts How do these costs vary as Q varies? Why isn’t item cost for the year included?

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Holding Cost $ (Q/2)×H Holding cost increases as Q increases . . . Q

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**Ordering costs per year decrease as Q increases**

$ Ordering costs per year decrease as Q increases (why?) (Q/2)×H (D/Q)×S Q

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**Total Annual Costs and EOQ**

EOQ at minimum total cost

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EOQ Solution When the order quantity = EOQ, the holding and setup costs are equal

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Sample Problems Pam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers is 16,000. The annual holding cost per unit is $2.50 and the cost to place an order is $50. What is the economic order quantity? Using the same holding and ordering costs as above, suppose demand for TricoFlexers doubles to 32,000. Does the EOQ also double? Explain what happens. Answers: EOQ = 800; 1,131 (goes up by the square root of 2)

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**EOQ tells us how much to order...**

…but when should we order? Reorder point and safety stock analysis

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Safety Stock When both lead time and demand are constant, you know exactly when your reorder point is ... Q R L

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**Safety Stock II Under these assumptions:**

Reorder point = total demand during the lead time between placement of the order and its receipt. ROP = d × L, where d = demand per unit time, and L = lead time in the same time units

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**Safety Stock III (Uncertainties)**

But what happens when either demand or lead time varies? Q R L1 L2

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**Safety Stock IV What causes this variance? Average demand**

during lead time

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**Uncertainty Drivers The variability of demand**

The variability of lead time The average length of lead time The desired service level 2) and 3) are determined by a company’s choice of supply chain partners

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Safety Stock Additional inventory beyond amount needed to meet “average” demand during lead time Protects against uncertainties in demand or lead time Balances the costs of stockouts against the cost of holding extra inventory

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Shown Graphically … Now, what is the chance of a stockout? 7% 93%

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**Recalculating the Reorder Point to include Safety Stock**

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Determining “z” z = number of standard deviations above the average demand during lead time The higher z is: The lower the risk of stocking out The higher the average inventory level What is the average inventory level when we include safety stock? Average inventory plus safety stock level

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Determining “z” Typical choices for z: z = 90% service level z = 95% service level z = 99% service level What do we mean by “service level”?

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**Reorder Point + Safety Stock Formula:**

What happens if lead time is constant? What happens if the demand rate is constant? What happens if both are constant? If you wanted to reduce the amount of safety stock you hold, what is your best option?

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**Problems I One of the products stocked by Sam’s Club is SamsCola.**

During the slow season, the demand rate is approximately 650 cases a month, which is the same as a yearly demand rate of 650×12 = 7,800 cases. During the busy season, the demand rate is approximately 1,300 cases a month, or 15,600 cases a year. The cost to place an order is $5, and the yearly holding cost for a case of SamsCola is $12.

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**Problems II According to the EOQ formula:**

How many cases of SamsCola should be ordered at a time during the slow season? How many cases of SamsCola should be ordered during the busy season? Slow season: 81 cases Busy season: 114 cases

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Problems III During the busy season, the store manager has decided that 98 percent of the time, he does not want to run out of SamsCola before the next order arrives. Use the following data to calculate the reorder point for SamsCola. Weekly demand during the busy season: 325 cases per week Lead-time: 0.5 weeks Standard deviation of weekly demand: 5.25 Standard deviation of lead-time: 0 (lead-time is constant) Number of standard deviations above the mean needed to provide a 98% service level (z): 2.05 Answer: 170 cases

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**Quantity Discounts I What effect will quantity discounts have on EOQ?**

D = 1,200 units (100×12 months) H = $10 per unit per year S = $30.00 ordering cost Order Size Price $35.00 90 and up $32.50 Note: When H is a cost based on a percent of the value of the item, these calculations become more complicated, but are done in the same way.

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**Quantity Discounts II 1. Calculate the EOQ for the non discount price:**

2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ...

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**Quantity Discounts III**

Compare total holding, carrying, AND item cost for the year at: Each price break The first feasible EOQ quantity Do you understand why we must now look at item cost for the year?

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**Quantity Discounts IV Total costs at an order quantity of 85:**

(85/2)×$10 + (1200/85)×$ ×$35.00 = $ $ $42,000 = ?? Total costs at an order quantity of 90: (90/2)×$10 + (1200/90)×$ ×$32.50 = $ $ $39,000 = ?? Quantity 85: $42,848.53 Quantity 90: $39,850

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Conclusions: When all costs are considered, it is cheaper to order 90 at a time and take the price discount. When there are volume discounts, the EOQ calculation might be infeasible or might not result in lowest total cost. If holding cost is a percentage of the item value (a common practice for more expensive items), analysis is more complex, but done the same way

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**Single-Period Inventory (When safety stock is not an option)**

Inventory is perishable Newspapers, periodicals Fresh food, Christmas trees Must balance costs of Being short = profit lost Having excess = item cost + disposal cost – salvage value Requires a target service level that best balances shortage and excess costs

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Target Service Level Sets expected shortage cost = expected excess cost Or (1–p) × Cshortage = p × Cexcess Where p = probability of enough units to meet demand, (1–p) = probability of shortage Hence solving for p where the top equation is true provides the target service level SLT = Cshortage / (Cshortage + Cexcess)

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**Target Stocking Point Must know how demand is distributed**

Is it roughly the same every day? Are there different demand distributions? In all cases, develop the cumulative probability distribution for the demand levels in order of increasing demand and select demand level whose corresponding cumulative probability is nearest to the target service level.

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Text Example for SLT = 65%

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**Inventory in the Supply Chain**

Bullwhip Effect Small demand changes large order variations Inventory Positioning Cost and value increases, flexibility decreases down the supply chain where do we hold inventory? Transportation, Packaging, Material Handling Physical size and quantity of lot, how it is packaged, handling equipment needed,and disposal of packaging are all factors in choosing appropriate supplier and distribution process

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**Demand versus Order Size (Bullwhip Effect)**

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**Case Study in Inventory Management**

Northcutt Bikes: The Service Department

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**Supplement ABC Classification Method**

IDEA Companies have thousands of items to track Methods like EOQ only justifiable for most important items.

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**ABC Method Determine annual $ usage for each item**

Rank the items according to their annual $ usage Let: Top 20% “A” items roughly 80% of total $ Middle 30% “B” items roughly 15% of total $ Bottom “50% “C” item roughly 5% of total $

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**ABC Analysis Example Total $ Usage = $98,500 Item Cost Demand $ Usage**

$46 200 $9,200 B2 $40 10 $400 C3 $5 6680 $33,400 D4 $81 100 $8,100 E5 $22 50 $1,100 F6 $6 $600 G7 $176 250 $44,000 H8 150 $900 I9 $10 $100 J10 $14 $700 Total $ Usage = $98,500

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**Ranking by Annual $ Usage**

Item $ Usage Cumulative $ Usage % of Total $ Usage Class G7 $44,000 44.67% A C3 $33,400 $77,400 78.58% A1 $9,200 $86,600 87.92% B D4 $8,100 $94,700 96.14% E5 $1,100 $95,800 97.26% H8 $900 $96,700 98.17% C J10 $700 $97,400 98.88% F6 $600 $98,000 99.49% B2 $400 $98,400 99.90% I9 $100 $98,500 100.00%

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